Monday, 7 May 2012

On the Shoulders of Merchants: Gresham, Stevin and science

When the short lived Edward VI became king of England in 1547, the nation’s wealth was based on the export of one commodity, wool, out of London and into Antwerp [Stone, 1947, p 104]. Edward was succeeded by his Catholic sister Mary, who married Philip of Spain but died young and was followed by her Protestant sister, Elizabeth, in 1559. During the turbulent times of Elizabeth’s reign, security, and not prosperity, became the main object of Tudor economics.

Central to managing the economy was Thomas Gresham. Born in London around 1519 into a prominent merchant family, Gresham was appointed the ‘Royal Factor’ at Antwerp in 1551. The role of the Factor was to arrange for Antwerp speculators to lend money to the English crown, mainly to cover the costs of war. The loans were typically short term, lasting six or twelve months, and so the Factor had to continually re-negotiate the agreements. Gresham realised that key to the process was ensuring that the exchange rate was favourable, and to this end he managed the trade in English Bills of Exchange, making sure they were in short supply, and so more valuable, in Antwerp, when he wanted to borrow money. This was no mean feat and, despite falling out of favour with Mary, Gresham became an inﬂuential member of the Elizabeth’s court.[Burgon, 2004, [pp9-12], [Johnson, 1940, pp 594-600]

Gresham moved in the circle of Elizabeth’s Secretary of State, William Cecil, Lord Burghley, advising him to develop the English armaments industry in preparation for war [Burgon, 2004, [pp9-12]. Apart from the likes of the spy Francis Walsingham, and the writers Christopher Marlowe and Philip Sydney, others in the group were the mathematicians Robert Recorde and John Dee. Recorde, one time Controller of the Royal Mint, is famous for introducing the “=” sign into mathematics, in the book The Whetstone of Witte dedicated to the Governors of the Muscovy Trading Company that had created to develop English the wool trade with Russia. John Dee is notorious today for being a ‘magician’, but during his lifetime his fame was based principally on his mathematical knowledge, which included the ability to cast horoscopes, Dee had worked with Cardano when the Italian was in London. Dee was also an adviser to the Muscovy Company and worked with Gresham on commercial ‘projects’ to “make this kingdome ﬂourishing triumphant, famous and blessed” [Hadden, 1994, p 109]. This system, where the economy was run to ensure a nation controlled its own armaments industry and accumulated gold or silver, became known as ‘mercantilism’ and would dominate Europe until the Enlightenment.

In 1565 Gresham established the Royal Exchange, modelled on Antwerp’s Bourse, to trade commodities and currencies. He returned to London in 1567, as the Dutch Revolt became inevitable, and in 1579 he died of a stroke. In his will, Gresham left all the revenues from the buildings that made up the Royal Exchange along with his mansion on Bishopsgate to the Company of Mercers and the City of London. In return, these two bodies were to support seven academics, in Law, Rhetoric, Divinity, Music, Physics, Geometry and Astronomy, to be housed in his mansion. The properties were held by Gresham’s widow until she died in 1596, and Gresham’s College opened in 1598. According to the historian, Francis Johnson

The opening of Gresham College was the culmination of a long eﬀort in Elizabethan England to bring about the establishment of a permanent, endowed foundation which would oﬀer instruction and further research in the mathematical sciences and provide a convenient rallying point for all who were concerned with promoting progress in the practical application of these sciences to useful works. [Johnson, 1940, p 424]

Remarkably, the mathematical chairs at Gresham College preceded those at Oxford, where the Savilian chair was established in 1619, and Cambridge would wait until 1663 to create the Lucasian chair in mathematics. [Johnson, 1940, pp 423–424]

Across the Channel, one of the most signiﬁcant characters emerging out of the turmoil of the Dutch Revolt was Simon Stevin. Born in 1548 in Bruges, like Gresham, Stevin had originally trained in the abbaco tradition and worked as a merchant’s clerk in Antwerp then as a tax oﬃcial back in Bruges, where he wrote his ﬁrst book Tafelen van Interest (‘Tables of interest’) which he published in 1582, before moving to the University of Leiden in 1583. He taught mathematics at the University, one of his students being Prince Mauritz of Nassau, who had succeeded his assassinated father William the Silent as leader of the Dutch Revolt. Stevin was involved in the the Dutch Republic’s government, becoming Inspector of Dyke’s, an important post in the low countries, in 1592, and Quartermaster-General in 1604, advising Mauritz on tactics including how to breach dikes in order to ﬂood the land and hinder the Spanish. [Sarton, 1934]

One of Stevin’s most inﬂuential posts was as the director of the Dutch Mathematical School, established in 1600 by Mauritz to train military engineers. In 1605 Stevin published a textbook for the School, the ‘Mathematical Tradition’, which was a comprehensive overview of mathematics and included a whole section on ‘Accounting for Princes in the Italian manner’. In a very short period, the Dutch Mathematical School became the centre for merchant’s training in north western Europe. This in turn forced the authorities at the University of Leiden, which provided the School with its facilities, to take practical sciences, in particular mathematics, a bit more seriously [Poitras, 2000, pp131–132].

The signiﬁcance of the School was that, up to this point, universities had maintained the Aristotelian view of mathematics as being only concerned with the quadrivium, abstract arithmetic and geometry or astronomy applied to calculating dates, and music [Dear, 2001, p 17]. These were not very prestigious in the scholastic world and mathematicians were generally poorly paid [Dear, 2001, p 104]. The incorporation of the practical mathematics curriculum into the University of Leiden can be seen as a conclusion of the integration of the abbaco and scholastic traditions that had begun with Pacioli a century earlier.

Stevin was particularly remarkable in that he wrote almost exclusively in Dutch or French, but rarely in Latin. This meant that his books were read widely and a consequence of the popularity of his writing has had a lasting eﬀect on the Dutch language; it is one of the few European languages that has its own, rather than using Latin or Greek, words for many mathematical terms. For example the Dutch for mathematics is wiskunde, which literally means ‘the art of certain knowledge’. In writing in the vernacular Stevin was disassociating himself with both the scholastic and humanist traditions, which were so enamoured with Greek and Roman ideas, and emphasising the practical usefulness of science in everyday life.

As well as being active in government and administration, Stevin was also a proliﬁc scientist, addressing both theoretical and practical problems and the economic historian Philip Mirowski has suggested that Stevin’s bookkeeping inspired his physics [Mirowski, 1989, p 121]. Practically he designed a new, more eﬃcient, windmill, based on mathematics, to drain the land and power Dutch industry, creating a wind powered industrial revolution. Theoretically, he showed that Aristotle’s science was fundamentally ﬂawed.

One revolutionary step Stevin took was in regard to the fundamental nature of numbers. The Hellenistic mathematicians had taken the number ‘1’, unity, to be the generator of numbers; ‘3’ is made up of three unities, and so on which related to Aristotle’s theory of measuring using the minimum unit of the thing being measured. Stevin explicitly states that ‘1’ is a number like any other number, because mathematical operations can be performed on it, just as on other numbers. He then makes a startling observation for the time, numbers are continuous, there are no gaps in them as there are gaps between 1 and 2 of a half and a quarter, or a quarter and an eighth, and so on [Katz, 1993, p 347].

Another example, is concerned with the nature of motion. In his Physics Aristotle starts by discussing the concept of motion and then, having pinned down the idea through reasoning, or logic, goes on to deduce the properties of moving bodies, including the belief that heavier objects fall faster than lighter objects [Hall, 1962, p 161]. In an experiment that is usually attributed to Galileo dropping things from the Tower at Pisa some years later [Hall, 1962, p 78], Stevin disproved this core belief of Aristotle. The Dutch bookeeper was less interested in what ought to happen, but rather what actually happened.

Another result usually associated with Galileo was concerning the tides. Galileo’s original title for the the ‘Two World Systems’, the book that got him into trouble with the Catholic Church, was Dialogue on the Ebb and Flow of the Sea, because, as a consequence of the Copernican theory and mathematics, Galileo argued that there would be one tide a day. When he sent the book to the Church for approval, he was told to change the title because every European sailor knew that there were two tides a day. For the Church of the time, built on Aristotle, Galileo’s use of mathematics to describe reality was not just philosophically wrong, it also resulted in absurd conclusions. The historian, Harold Brown puts a modern slant on the issue

Galileo’s attempt to account for the tides as a result of the combined daily and annual motion of the earth, and his belief that this argument provided a physical proof that the earth moves, stands as something of an embarrassment.Brown [1976]

Galileo was often preceded by Stevin, and it is ironic that Stevin had more successfully addressed the theory of tides in 1608 based on the Moon’s inﬂuence [Sarton, 1934, p 280]. Galileo’s error was in ignoring the Moon and attempting to explain the tides by the Earth’s movement around the Sun – a little too Heliocentric.

References

H. I. Brown. Galileo, The Elements and the Tides. Studies in History and Philosophy ofScience, 7(4), 1976.

Twitter

Followers

Subscribe

About Me

I am a Lecturer in Financial Mathematics at Heriot-Watt University in Edinburgh. Heriot-Watt was the first UK university to offer degrees in Actuarial Science and Financial Mathematics and is a leading UK research centre in the fields.

Between 2006-2011 I was the UK Research Council's Academic Fellow in Financial Mathematics and was involved in informing policy makers of mathematical aspects of the Credit Crisis.